Highest Common Factor of 690, 560, 689 using Euclid's algorithm

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 690, 560, 689 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 690, 560, 689 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.

Consider we have numbers 690, 560, 689 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b

Highest common factor (HCF) of 690, 560, 689 is 1.

HCF(690, 560, 689) = 1

HCF of 690, 560, 689 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of:

Highest common factor (HCF) of 690, 560, 689 is 1.

Highest Common Factor of 690,560,689 using Euclid's algorithm

Highest Common Factor of 690,560,689 is 1

Step 1: Since 690 > 560, we apply the division lemma to 690 and 560, to get

690 = 560 x 1 + 130

Step 2: Since the reminder 560 ≠ 0, we apply division lemma to 130 and 560, to get

560 = 130 x 4 + 40

Step 3: We consider the new divisor 130 and the new remainder 40, and apply the division lemma to get

130 = 40 x 3 + 10

We consider the new divisor 40 and the new remainder 10, and apply the division lemma to get

40 = 10 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 690 and 560 is 10

Notice that 10 = HCF(40,10) = HCF(130,40) = HCF(560,130) = HCF(690,560) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 689 > 10, we apply the division lemma to 689 and 10, to get

689 = 10 x 68 + 9

Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 9 and 10, to get

10 = 9 x 1 + 1

Step 3: We consider the new divisor 9 and the new remainder 1, and apply the division lemma to get

9 = 1 x 9 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 10 and 689 is 1

Notice that 1 = HCF(9,1) = HCF(10,9) = HCF(689,10) .

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Frequently Asked Questions on HCF of 690, 560, 689 using Euclid's Algorithm

1. What is the Euclid division algorithm?

Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.

2. what is the HCF of 690, 560, 689?

Answer: HCF of 690, 560, 689 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 690, 560, 689 using Euclid's Algorithm?

Answer: For arbitrary numbers 690, 560, 689 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.